The Baker-Campbell-Hausdorff formula in the free metabelian Lie algebra
arXiv:math/0606330
Abstract
The classical Baker-Campbell-Hausdorff formula gives a recursive way to compute the Hausdorff series H=ln(e^X e^Y) for non-commuting X,Y. Formally H lives in the graded completion of the free Lie algebra L generated by X,Y. We present a closed explicit formula for H=ln(e^X e^Y) in a linear basis of the graded completion of the free metabelian Lie algebra L/[[L,L],[L,L]].
10 pages, the paper was completely reworked. The metabelian BCH formula is interpreted as a linear part of a deeper formula for ln(e^X e^Y)